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I believe this is due to the fact that atoms with lower ionization energies are prone to have more open spaces that need to be filled with electrons, or less of a complete octet. So putting that as the central atom makes the Lewis structure easier since this atom would have more access to forming multiple bonds with different atoms to fill their octet.
I think that we choose an atom with the lowest ionization energy as the central atom because those are the atoms that have electrons that are less tight.It makes it easier to add more electrons to the atoms to make it less likely to remove electrons and have more bonds.
The central atom has to bond with more atoms around it - a central atom with lower ionization energy would more readily share its electrons (since it's not "holding onto" its electrons as tightly). Also, atoms with higher ionization energy usually have more lone pairs, which would cause more repulsion and instability if it were in the center.
I think it’s also important to remember that this is just a guideline. Finding formal charges might be the best way to determine which atom should be the central atom. Consider the case for ONF (from problem 3.33). Although oxygen technically has the lowest ionization energy of the three elements, it is actually not the central atom. N would be the central atom in this case because of more harmonious formal charge.
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